Yeah caird is right. It's a bit of notational abuse, but we call the number after w, w+1, then w+2 etc. the number past all w+n is called w+w or 2w, then there is 2w+1, 2w+2, all the way to 3w, then 4w, 5w etc. and so after all of those you get w*w or w^2, and you can continue going from there ... w^w is the number after all polynomials of w. And of course there are bigger ordinals after it (like w^w+1).

@ngn All countable cardinals are the same (aleph_0), but not all countable ordinals are the same.

so basically, we just took "infinity" and made it into an actual "number" that you can do arithmetic with?

Yep.

this is really cool and quite challenging to get my head around

just wait until you discover the fast growing hierarchy

I mean we can't do all arithmetic with it. For example you can subtract 1 from it. In fact despite the symbols used we aren't really adding anything in something like w^2+w+3.

@WheatWizard is wikipedia wrong when it says w^w is countable? intuitively it seems |w^w| should be larger than |w|

w^w is countable. The size of all number smaller than w^w is exactly the same as w.

Proof: There are a countable number of strings. All polynomials of w can be written in a string (e.g. "w^5+6w^3+87"), therefor the polynomials of w are countable. All ordinals less than w^w are polynomials of w.

What's the smallest cardinal that comes after all omega cardinals? epsilon zero?

Despite some questionably accurate statements about the continuum hypothesis, this video is still excellent for getting started with infinite ordinals and cardinals.

@WheatWizard ok, i think i got it

@cairdcoinheringaahing epsilon 0 is still a countable ordinal, so it is smaller than w_1, the smallest uncountable ordinal.

@rak1507 Is there anything that can be done about the suspended users creating havoc in chat rooms? I saw your comment in math.se "Cafe and Tavern" chatroom. It seems @hyper-neutrino is a mod here. I know you've done everything, @hyper, on your end in terms of suspending a troublesome user. And perhaps the best policy is to merely ignore them when interfering in chatrooms across the SE network.

seems like even talking about it is discouraged...

@hyper-neutrino understood. I saw your message in the Cafe. Got it.

Related Mother Meta

@WheatWizard ok, so if w^w is countable, then |w^w| = |w| = aleph0, and your cmc is simply asking for "more" than |w| steps

Not more steps per-se but to end later. w+1 is still after w, so if you made a machine that halted at step w^w+3 or something that would work.

ah..

so "takes longer to halt" should be understood in terms of ordinals, not cardinals

Indeed.

Is CodeGolf a chilled version of stackoverflow?

That's kinda complicated :p

no, it's not really a question and answer site, more a puzzle site

Technically, no

In short, no

^ This might help

@cairdcoinheringaahing Technically?

I understand. Very interesting.

@vitamind We started out on SO with people posting [code-golf] questions there, and a bunch of people disliked the more casual aspect of it. This caused people to suggest branching off into a new site, which is what we did. It used to be very lax and "hey, look at this loophole, aren't I funny?" but we've spent 10 years refining the site

But we are way more laid back than SO

Much more laid back

the site has grown so much from the early days when code-trolling was a thing (ಠ_ಠ)

Code trolling was only 7 years ago :P

I think there are some ways in which SO is more chill.

CMV: All code golf is code trolling :P

@WheatWizard I'm not that familiar with SO tbh, what are the more chill ways?

@WheatWizard "40 is the biggest number on earth in terms of surface area" :)

I mean we are pretty anal about observable criteria. SO questions can be pretty vague as opposed to ours in which you must be able to objectively determine if an answer is valid and rank it.

tbf my perspective is a little skewed since I believe I might be the most prolific close voter on the site.

Well SO also allows partial answers as long as they're useful in some way

@ngn meanwhile in bulgaria

lol what

@WheatWizard How many VTCs have you cast?

Over 1,000.

I think you (anyone who clicks) can see the exact number here

huh, I've only cast 188.

581 here

data.stackexchange.com/codegolf/query/1379134/…

This is certainly wrong, but it does place me at #1 so I probably am pretty high up there.

@WheatWizard It doesn't register deleted posts

And probably posts for which the voting failed?

No, I think it does register votes cast rather than posts closed, so even if you are the only VTC on a post, it should register it

Hm I wonder how many states I need to get w_1.

@WheatWizard can you explain what the notation in the ittm diagram means?

that paper is too long for my attention span..

Sure, yeah. The exact notation I used probably isn't specifically discussed in the paper anyway.

Where are you coming from? Is there a specific bit you don't get or have you never seen a diagram like this before at all?

@WheatWizard i've seen diagrams of finite-state machines where "q" are the states, and the arrows are transitions, and the transitions consume input

i'm supposed to be familiar with turing machines too but last time i studied them was 20 years ago

does "1 -> 0,L" mean "if you're on a 1, then write a 0 and move left"?

Yes.

what's the initial state of the tape?

All 0s.

If no transition can be taken the program halts.

how long is the tape? :)

so from my understanding, starting at index 0, the q1 to q2 transition moves to index 1, then the q2 to q3 transition writes a 1, then the q3 self-loop writes a 0, then the other q3 self-loop infinitely writes 0s to the same cell?

Infinite to the right. But this particular machine never goes past cell 3.

@hyper-neutrino That is the finite behavior yes.

ah. how does the infinite behavior change exactly? since i don't see a transition from q3 back

The "idea" for this machine is that cell 2 blinks on at every nw+2 for natural n. This means that the limsup of cell 2 as we go to w^2 is 1, so when we reach w^2 cell 2 is on, and we turn it off an blink cell 1, and this process repeats with cell 1 blinking on for each step w^n+3. So at w^w the limsup for cell 1 is 1 and the machine halts.

just to clarify, we are starting at cell 1?

Oh yeah. Am I a bad computer programmer for using 1 indexing :)

nah just making sure ;) honestly 1-indexing is nicer for a lot of things because then the "not found" index is falsy :P

@hyper-neutrino Whenever we hit a limit ordinal the machine gets put in the "limit state" (q1), so after it loops in q3 forever it snaps over to q1.

oh, that's what the start/limit means

okay that makes a lot more sense, lol. i wasn't seeing how we were getting from q3 back to q2

i didn't realize that either

Here's an animation of a much stupider machine that might be a bit helpful.

that makes a lot more sense

just wondering then - if it's 1 half the time and 0 half the time, why is 1 the state chosen at the limit?

We take the "limsup" which is a fancy word, but in this case it means if there is a limit it is set to that, if there is no limit it is always 1. It is ultimately arbitrary. We could also choose to take the liminf and have it be 0 and it wouldn't really effect too much.

oh, i see. so limsup vs liminf is arbitrary as long as we pick one and stay consistent

Exactly.

okay, thanks. that makes more sense

→ 28 messages moved to Trashcan

Yeah sorry, I just sort of jumped into things, all this is in the paper, and I wasn't sure how much people knew.

@hyper-neutrino I think moving those to Trash would've been better, it could've been good to keep a public record of that. Trashcan's more for stuff no-one needs to see again IMO :)

Here's another animation I have been working on.

@cairdcoinheringaahing That's valid. I usually do that to not send invitations to trash. Also IMO some stuff said was arguably flaggable and i'd rather toss it in the private records

@hyper-neutrino Fair enough :)

maybe i'll make a gallery trash room to have public records without spamming people with invitations

That's a good idea

Isn't Trash a gallery room?

If not, shouldn't it be?

Wouldn't that make it so that non-write-perms people couldn't move stuff there?

No, you can move posts to whatever room IITC

oh wait. i think you're right

@cairdcoinheringaahing then you could just create a room and move messages in to get around read only restrictions

granted, you'd probably get suspended for that if it were possible

But it's still probably not since it's like putting a button on the homepage that automatically spams the site then telling people not to use it :p

@hyper-neutrino Mind making your office room a gallery, I want to just test this :P

Nope, can't move it there :(

as expected :P in that case, i guess i can make a gallery trash that ROs can request access to so they can throw trash there but will get invited to should they get their messages trashed

actually i don't want to deal with write access requests. maybe i'll just make a mod-only gallery trash :P doubt it'd get used. i just don't want to annoy people unnecessarily with trash invitations especially if they're already irritated by me

I suppose if you've been posting trash-worthy messages, the ping is a punishment for it :P

@cairdcoinheringaahing well sometimes i trash replies to trash worthy messages from users who don't deserve said punishment :p

Finally get a good nether, very open and navigatable, bastion right across a lava lake, then I misjudge a jump and land right in it :|

The "good nether" is still there, no? Was it hardcore or something?

I'm practicing speedrunning

Ah

That's uber-hardcore

Imagine speedrunning. Made by the "I've only ever beat the Ender dragon once in an actual survival game" gang D:

Any Feed Back?

@cairdcoinheringaahing Keyword is definitely "practicing", I've still got a long way to go before I can consistently not mess up each individual part of each run :p

@Adám You might want to propose APL here, if applicable (I'm not sure for which kind of projects APL is typically used)

@Bubbler Both look good

Trying Filtered Seed Glitchless, it guarantees you a good seed each time so it's good for practice.

\o/ \o/